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Discrepancy between my work and book's [Static Fluid/Pressure]

  1. Jun 1, 2013 #1
    The book (Example 13-3):
    XmnYGsI.jpg

    My attempt:
    GgSrM7Q.jpg

    My confusion is in why they are starting their height at 1.0 meters above the surface of the water and then getting a y_2 value of 2.0 meters. That's the discrepancy that's giving me a different value than the book's. It never says in the question to do that, and I'm baffled as to how I am supposed to know.

    Thanks in advance for the help.
     
  2. jcsd
  3. Jun 1, 2013 #2

    TSny

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    Hello.

    In P = ρgh, h denotes the depth below the surface of the water. h is also your integration variable. What is the value of h at the top of the window? At the bottom of the window?

    [EDIT: Note that the window is submerged below the surface of the water.]
     
  4. Jun 1, 2013 #3
    h = 0.0 meters at the top and h = 1.0 meters at the bottom of the window.
     
  5. Jun 1, 2013 #4

    TSny

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    The widow is embedded in the side of the aquarium with the top of the window 1.0 m below the surface of the water.
     
  6. Jun 1, 2013 #5
    Ah, I see. I wish they would explicitly state these things in the question as it seems I am unable to derive them from the pictures, haha. Well, they don't write the books for me!

    Thanks TSny! I will approach this problem again. Do you think I can keep my origin at the top of the window and change my bounds to -1m to +1m? It seems this will still give me an incorrect value and I may have to change my origin to the top of the water tank.
     
  7. Jun 1, 2013 #6

    TSny

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    Suppose you introduce a y-axis going vertically downward. You can certainly choose the origin of y to be at the top of the window. Then you would need to think about how to express the depth h in terms of y.

    [EDIT: You could then integrate from y = 0 to y = 1.]
     
  8. Jun 1, 2013 #7
    Alright, it seems you have nailed the source of confusion on the head. I will have to redraw my diagram and rewrite my integral thinking about the relation of h and y.

    edit: I was way overthinking this. I reintegrated with new bounds and it comes out perfectly. Thanks a bunch, TSny!
     
    Last edited: Jun 1, 2013
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